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Q: mathematical formula ( Answered,   3 Comments )
Subject: mathematical formula
Category: Science > Math
Asked by: radom-ga
List Price: $10.00
Posted: 02 Oct 2002 01:19 PDT
Expires: 01 Nov 2002 00:19 PST
Question ID: 71521
what is a formula that calculates the number of possible combinations
of three members from n numbers, where n is a real number.
Subject: Re: mathematical formula
Answered By: johnny_phoenix-ga on 02 Oct 2002 02:31 PDT
the general formula is               n!
                         n_C_k = ----------
                                 k!(n - k)!

where n is a real number and k is the number selected (in your case 3)

"3!" is for example 3x2x1
"n!" would be n x(n-1)x(n-2)and so on until n reaches 1.

so your finished formula would be   

                         n_C_3 = ----------
                                 3!(n - 3)!

For more explantion and examples on how this works, check out 

Ask Doctor Math

This is a very easy to understand page that will help you understand
how the formula works.


suppose we want to find out the number of ways we can arrange 1 2 3.
you can write them all out and know it reaches 6 or you can use the

3_n_3 =          3!
              3! (3-3)!

      =       3x2x1
            3x2x1 x(0)

       =       6

       =       6

I hope this helps. 

Johnny Phoenix

Clarification of Answer by johnny_phoenix-ga on 02 Oct 2002 07:17 PDT
oops, well spotted "0!" = 1 not 0, apologies.

lol @ asterisk man...good questions indeed, not sure we're allowed to
answer them for free though lol.
Subject: Re: mathematical formula
From: chulan-ga on 02 Oct 2002 05:26 PDT
A small typo, it is (3-3)!, which is (0)! which equas 1.
This means the result from this formula is 1 rahter than 6.
An thats correct as the combination formula ignores the order of the
being combined.  So '123' is considerd the same as '321'.

If you want to count the different orderings then you want the
permutation formula which is

n_P_k = -------- 
        (n - k)!

Which in you case would give the answer of 6.

Subject: Re: mathematical formula
From: asterisk_man-ga on 02 Oct 2002 06:12 PDT
Not to be picky but isnt n! usually only defined for non-negative
The question asked for n to be a real number. Most likely the question
asker did not intend to select 3 items out of a real number.
what does 24.5421 choose 3 mean anyway? what is 24.5421! ? (windows
calculator says 24.5421! = 3534876327450063425731321.6696764 but dont
ask me where they come up with that)
Anyway, I'll still agree with the answer other than the "real" part
(and that x/0=x part (o:  ). If someone can point out the answers to
the two questions I've posed I'd be interested in them...though not
enough to make it a question of my own (o:
Subject: Re: mathematical formula
From: gsiaf-ga on 03 Oct 2002 06:06 PDT
search for Gamma function .
Eg. .
HTH & Bye,                                                            \/#_|{>/

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